Related papers: Maxwell's equations with hypersingularities at a n…
The space-time curvature carried by electromagnetic fields is discovered and a new unification of geometry and electromagnetism is found. Curvature is invariant under charge reversal symmetry. Electromagnetic field equations are examined…
The homogenization of eigenvalues of non-Hermitian Maxwell operators is studied by the H-convergence method. It is assumed that the Maxwell systems are equipped with suitable m-dissipative boundary conditions, namely, with Leontovich or…
We consider the Cauchy problem for the (non-linear) Maxwell-Charged-Scalar-Field equations with spherically symmetric initial data, on a sub-extremal Reissner--Nordstr\"{o}m or Schwarzschild exterior space-time. We prove that the solutions…
We present and discuss new families of primary hair charged black hole solutions in asymptotically anti-de Sitter space in three dimensions. The coupled Einstein-Maxwell-scalar gravity system, that carries the coupling $f(\phi)$ between the…
New simple field equations are proposed (Eqs. (5)), unifying Maxwell's equations of the Standard Model electrodynamics (after the electroweak symmetry is spontaneously broken) with the dynamics of cold dark matter. The cold dark matter is…
We study a free scalar field $\phi$ in a fixed curved background spacetime subject to a higher derivative field equation of the form $F(\Box)\phi =0$, where $F$ is a polynomial of the form $F(\Box)= \prod_i (\Box-m_i^2)$ and all masses…
We study the cubic vertices for Maxwell-like higher-spins in flat and (A)dS background spaces of any dimension. Reducibility of their free spectra implies that a single cubic vertex involving any three fields subsumes a number of couplings…
We study Friedmann--Robertson--Walker models with a perfect fluid matter source and a scalar field nonminimally coupled to matter. We prove that a general class of bounded from above potentials which fall to minus infinity as the field goes…
We make use of the conformal compactification of Minkowski spacetime $M^{\#}$ to explore a way of describing general, nonlinear Maxwell fields with conformal symmetry. We distinguish the inverse Minkowski spacetime $[M^{\#}]^{-1}$ obtained…
We extend all known black hole no-hair theorems to space-times endowed with a positive cosmological constant $\Lambda.$ Specifically, we prove that static spherical black holes with $\Lambda>0$ cannot support scalar fields in convex…
Although high-order Maxwell integral equation solvers provide significant advantages in terms of speed and accuracy over corresponding low-order integral methods, their performance significantly degrades in presence of non-smooth…
We study the quasilinear Maxwell system with a strictly positive, state dependent boundary conductivity. For small data we show that the solution exists for all times and decays exponentially to $0$. As in related literature we assume a…
In this paper, we consider inverse time-harmonic acoustic and electromagnetic scattering from locally perturbed rough surfaces in three dimensions. The scattering interface is supposed to be the graph of a Lipschitz continuous function with…
We develop a quantization scheme for Maxwell's equations without source on an arbitrary four dimensional globally hyperbolic spacetime. The field strength tensor is the key dynamical object and it is not assumed a priori that it descends…
For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit…
In this paper, we propose fast solvers for Maxwell's equations in rectangular domains. We first discretize the simplified Maxwell's eigenvalue problems by employing the lowest-order rectangular N\'ed\'elec elements and derive the discrete…
This paper considers the inverse problem of scattering of time-harmonic acoustic and electromagnetic plane waves by a bounded, inhomogeneous, penetrable obstacle with embedded objects inside. A new method is proposed to prove that the…
The robustness of XRD methods for the determination of the lattice parameters of crystals is well established. These methods have been extended to helical atomic structures using twisted x-rays \cite{friesecke_twisted_2016}. Building on an…
In this paper, we consider an initial boundary value problem for Maxwell's equations. For this hyperbolic type problem, we derive guaranteed and computable upper bounds for the difference between the exact solution and any pair of vector…
The paper introduces a method to solve inverse problems for hyperbolic systems where the leading order terms are non-linear. We apply the method to the coupled Einstein-scalar field equations and study the question whether the structure of…